Ecuaciones Trigonométricas

18. 2cos2θ+3cosθ-2=0
2cosθ-1=0 2cosθ-1=0

θ= cos-112 θ=cos-1-2
θ1= 60°
θ2= 300°

19. cos2θ+2cosθ-3=0
(cosθ+1) (cosθ+3)=0θ=cos-11 θ=cos-1-3
θ1=0°
θ2= 360°

20. 2sin2θ-5sinθ+3=0
(2sinθ-3) (sinθ-1)=0
θ=sin32 θ=sin-11
θ1=90°
21.3tan2θ-4tanθ+3=0
(3tanθ-1) (tanθ-3)=0
θ=tan13 θtan3
θ1=30° θ1=60°
θ2=210° θ2=240°

22. 3tan2θ-4tanθ+3=03tan2θ+tanθ+3tanθ+1=0
(3tan2θ+tanθ)+(3tanθ+1)=0
(tanθ+1) (3tanθ+1)=0
θ=tan-11 θ=tan-1-13
θ1=135° θ1=120°
θ2=315°θ2=300°

23. 2sin2θ+(2-3)sinθ-3=0
2sin2θ+2sinθ-3sinθ-3=0
(2sin2θ+2sinθ)+(-3sinθ-3)=0
2sinθ(sinθ+1)-3(sinθ+1)=0
(2sinθ-3) (sinθ+1)=0
θ=sin-133 θ=sin-1-1θ1=60° θ1=270°
θ2=120°

24. 4cos2θ+(23-2) cosθ.3=0
4cos2θ+23cosθ-2cosθ-3=0
(4cos2 θ-2cosθ)+(23cosθ-3)=0
2cosθ2cosθ-1+3 (2cosθ-1)=0
(2cosθ+3)2cosθ-1=0
θ=cos-1-32 θ=cos-112
θ1=150° θ1=60°
θ2=210° θ2=300°

25. 3cot2θ-4cotθ+3=0(3cotθ-1)(1cotθ-3)=0
θ=

26. 2cos2θ-(1+25)cos θ+5=0
2cos2θ-cos θ-25cos θ+5=0
(2cos2θ-1cos θ)+(-25cos θ+5)=0
Cos θ(2Cos θ-1)+5(-25cos θ+5)=0
cos θ(-2cos θ-1)-5(2cos θ-1)=0
(cosθ-5)=0 (2cosθ-1)=0
θ=cos-15 θ=cos-112
θ1=60°
θ2=300°
27.3tan2θ+2tanθ-3=0
(3tanθ-1)(tanθ+3)=0
3tanθ-1=0 tanθ+3=0
θ=tan-113 θtan-1-3
θ1 =60° θ1=120°
θ2=240°...